A vehicle power transmission apparatus that includes a first electric motor, a second electric motor, a transmission member that is coupled to drive wheels and the second electric motor in a manner capable of transmitting power, a differential mechanism for distributing output of an engine to the first electric motor and the transmission member in a power transmission path between the engine and the drive wheels has been known. A technique for filling a backlash in such a vehicle power transmission apparatus in order to suppress generation of abnormal sound and the like has been suggested. For example, a control device for a vehicle that is described in Japanese Patent Application Publication No. 2013-169852 (JP 2013-169852 A) is one example thereof. In this technique, backlash filling torque for filling the backlash between two each of various gears on the power transmission path is output from the first electric motor at a startup in no load states of the first electric motor and the second electric motor. In this way, the generation of the abnormal sound at the startup of the vehicle can be suppressed.